Analysis Seminar

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Local smoothing estimate for the cone in $R^3$

Speaker: Hong Wang, IAS Princeton

Location: TBA

Date: Thursday, October 22, 2020, 11 a.m.

Synopsis:

If u is a solution to the wave equation on Rⁿ, a local smoothing inequality bounds ||u||_{L^p(Rⁿ x [1,2])} in terms of the Sobolev norms of the initial data. We prove Sogge's local smoothing conjecture in 2+1 dimensions. The proof uses induction on scales and an incidence estimate for points and tubes. This is joint work with Larry Guth and Ruixiang Zhang.

Notes:

This is an online talk via Zoom.